Other mistake: At the very beginning, when K disintegrates the alien Mikey, an MIB cover-up team arrives on the scene and approaches K at a distance of about ten meters (roughly 30 feet) ; whereupon K instructs them: "Give me a splay burn around the perimeter with holes at forty, sixty and eighty meters from right here! Thank you!" The team members disperse a scant few steps and use their flamethrowers and extinguishers on the cacti and undergrowth in the immediate area for five seconds. However, the distances K describes (forty, sixty, and eighty meters) would require the team laboriously dispersing hundreds of feet into the desert. But five seconds later, they're still only about 30 feet away from K when he says, "That's good! Thank you!" (00:07:55)
Other mistake: Jensen (U.S. Army West Point Officer) addresses himself as a Second Lieutenant, but upon closer inspection of his rank (bars on his shoulders), they are Silver. Silver bars indicate a 1st Lieutenant, Gold indicates a 2nd.
Continuity mistake: Before Kay erases the memories of the border patrol cops, he holds the neuralizer with his left hand while adjusting its knobs with his right hand. In the next shot, he's holding the neuralizer with his right hand.
Visible crew/equipment: When J is going to use the neuralyzer on K, on J's lenses you can notice that K has been replaced with a white screen used for lighting.
Other mistake: When K is deleting all documents belonging to Edwards (later J), his passport says he was born in Indiana, but his birth certificate says he was born in Manhattan, New York.
Other mistake: The first time the neuraliser is used it shows hours, weeks and years. But at the end of the film the lead character tells J to remember that it's "days, months, years." (00:08:06 - 01:24:52)
Suggested correction: Perhaps there are different models of neuralyzers.
I don't think arguing "perhaps such-and-such" is necessarily strong enough of a reason to correct a mistake. Nothing in the movie indicates they are different models, so it's probably best to assume they're the same.
